1. Field of the Invention
The present invention relates to a wavefront measuring method for unwrapping a two-dimensional phase image measured in interference measurement and a wavefront measuring apparatus using the wave front measuring method, which are primarily suitable to evaluate optical characteristics of an optical element.
2. Description of the Related Art
Conventionally, interference measurement has been performed to evaluate optical characteristics, such as surface shape and uniformity of an internal medium, of an optical element, such as a lens and a filter. In the interference measurement, an inspected wave (inspected light) transmitted through an inspected substance, such as an optical element, and a reference wave (reference light) as a standard are interfered to form four types of interference fringes as shown in FIG. 15A.
A two-dimensional phase image shown in FIG. 15B is calculated from interference fringe images, and unwrapping is performed to obtain an aberration of the inspected substance as a transmitted wavefront as shown in FIG. 15C.
Methods for calculating the two-dimensional phase image from the interference fringe images include a Fourier transform method and a fringe scanning method. Both methods include calculation of arctangent in the course of the methods, and the phases that are normally consecutive become wrapped phases in the range of −π to π due to the range of arctangent. The act of obtaining the normal consecutive phases (transmitted wavefront) from the wrapped phases is called unwrapping.
Various unwrapping methods are created based on the assumption that the normal phase change is basically smooth as described in Ghiglia Pritt Two-Dimensional Phase Unwrapping Theory, Algorithms, and Software (hereinafter, “Document 1”) and Japanese Patent No. 03423486 (hereinafter “Document 2”).
Document 1 describes methods dependent on the path, such as a Branch Cut algorithm, a Quality-Guided Path Following algorithm, a Mask Cut algorithm, and a Minimum Discontinuity algorithm, as methods for unwrapping from the wrapped phases. Document 1 also describes methods not dependent on the path, such as an Unweighted Least Squares algorithm, a Weighted Least Squares algorithm, and a General Minimum LP-Norm algorithm.
Document 2 describes a method of calculating a transmitted wavefront not from the wrapped phases, but from interference fringes. In this method, the inspected substance is rotated to count the changes in tone of the interference fringe points to thereby obtain phase changes from initial angles at each angle to calculate the transmitted wavefront.
However, in some cases, the number of interference fringes increase and the interference fringes become indistinct, so that the interference fringes cannot be resolved. If a two-dimensional phase image is calculated from an interference fringe image in which the indistinct interference fringes are photographed, the area with a 2π phase difference also becomes indistinct, so that unwrapping becomes difficult. In the conventional methods, unwrapping is performed by avoiding the indistinct area, or the indistinct area is interpolated by computation. Therefore, in some cases, the transmitted wavefront of the indistinct area cannot be calculated and falls off, and the reliability of the optical characteristic measurement of the optical element is reduced.